{"abstract":"A denominator with a0 = 2 reports reflection coefficients twice too large and false instability.","category":"Digital signal filters","checks":7,"contract":"Input the denominator [a0, a1, ..., an] as rational strings. Normalize by a0 (\"bad-a0\" if missing or 0), drop trailing zero coefficients, then step down: k = last coefficient, unstable if |k| >= 1, else a_i <- (a_i - k a_{p-i}) / (1 - k^2) for i < p. Return {\"stable\": bool, \"reflection\": [k strings so far]}.","evaluation_group":"w2-digital_signal_filters-schur-cohn-stability","failed_approach":"The attempted repair divides by |a0|, which flips every reflection coefficient sign when a0 < 0.","family":"w2-digital_signal_filters-schur-cohn-stability-leading-coefficient-normalization","id":"FA-91586","implementations":{"attempt":{"sha256":"e4a7feaa27208b4ed99d58a57d71c00db9e4e623ec468fce3bb3960d178a6d12","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a = [Fraction(v) for v in x]\n    if not a or a[0] == 0:\n        return 'bad-a0'\n    a = [v / abs(a[0]) for v in a]\n    while len(a) > 1 and a[-1] == 0:\n        a.pop()\n    ks = []\n    while len(a) > 1:\n        p = len(a) - 1\n        k = a[p]\n        ks.append(str(k))\n        if abs(k) >= 1:\n            return {'stable': False, 'reflection': ks}\n        a = [(a[i] - k * a[p - i]) / (1 - k * k) for i in range(p)]\n    return {'stable': True, 'reflection': ks}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: negative leading coefficient', ['-2', '1', '-1/2'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['regression: random denominator 3', ['-1', '-1/2'], {'stable': True, 'reflection': ['1/2']}], ['regression: random denominator 4', ['-1', '0', '5/4'], {'stable': False, 'reflection': ['-5/4']}], ['control: marginal pole on unit circle', ['1', '0', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: stable second order', ['1', '-1/2', '1/4'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['control: trailing zero coefficient', ['1', '1/2', '0'], {'stable': True, 'reflection': ['1/2']}], ['control: two trailing zeros', ['1', '-1/3', '0', '0'], {'stable': True, 'reflection': ['-1/3']}]], [['regression: random denominator 6', ['1/2', '1/8'], {'stable': True, 'reflection': ['1/4']}], ['regression: random denominator 11', ['-1', '0', '-1/2'], {'stable': True, 'reflection': ['1/2', '0']}], ['regression: random denominator 4', ['-1', '0', '5/4'], {'stable': False, 'reflection': ['-5/4']}], ['control: pole at -1', ['1', '1'], {'stable': False, 'reflection': ['1']}], ['control: unstable first order', ['1', '-3/2'], {'stable': False, 'reflection': ['-3/2']}], ['control: bad a0', ['0', '1'], 'bad-a0'], ['control: third order', ['1', '-1/2', '1/3', '-1/5'], {'stable': True, 'reflection': ['-1/5', '35/144', '-65/179']}]], [['regression: random denominator 19', ['-1', '3/4'], {'stable': True, 'reflection': ['-3/4']}], ['regression: random denominator 21', ['1/2', '3/4'], {'stable': False, 'reflection': ['3/2']}], ['regression: random denominator 28', ['-1', '1/8'], {'stable': True, 'reflection': ['-1/8']}], ['control: random denominator 0', ['-1', '0'], {'stable': True, 'reflection': []}], ['control: random denominator 1', ['1', '1/8', '1/8'], {'stable': True, 'reflection': ['1/8', '1/9']}], ['control: random denominator 2', ['1', '1/3', '1/3'], {'stable': True, 'reflection': ['1/3', '1/4']}], ['control: random denominator 5', ['1', '1/8', '1/3'], {'stable': True, 'reflection': ['1/3', '3/32']}]], [['regression: random denominator 24', ['2', '1/2'], {'stable': True, 'reflection': ['1/4']}], ['regression: random denominator 27', ['2', '1/3', '-1/2', '1/8'], {'stable': True, 'reflection': ['1/16', '-40/153', '28/113']}], ['regression: random denominator 34', ['-1', '1/2', '-1', '0'], {'stable': False, 'reflection': ['1']}], ['control: random denominator 7', ['1', '3/4', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 8', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}], ['control: random denominator 9', ['1', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 10', ['1', '-1/4', '1/8', '-1/2'], {'stable': True, 'reflection': ['-1/2', '0', '-1/4']}]], [['regression: random denominator 32', ['1/2', '-1/2'], {'stable': False, 'reflection': ['-1']}], ['regression: random denominator 34', ['-1', '1/2', '-1', '0'], {'stable': False, 'reflection': ['1']}], ['regression: random denominator 52', ['-1', '3/4', '5/4', '-1'], {'stable': False, 'reflection': ['1']}], ['control: random denominator 12', ['1', '5/4', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 13', ['1', '1/8', '1/8', '3/4'], {'stable': True, 'reflection': ['3/4', '1/14', '1/15']}], ['control: random denominator 14', ['1', '1/8', '5/4'], {'stable': False, 'reflection': ['5/4']}], ['control: random denominator 15', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"d3eed9d08be75dec4ae60455e08a58be62869f4ab8434cd00a4b152e4a307448","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a = [Fraction(v) for v in x]\n    if not a or a[0] == 0:\n        return 'bad-a0'\n    while len(a) > 1 and a[-1] == 0:\n        a.pop()\n    ks = []\n    while len(a) > 1:\n        p = len(a) - 1\n        k = a[p]\n        ks.append(str(k))\n        if abs(k) >= 1:\n            return {'stable': False, 'reflection': ks}\n        a = [(a[i] - k * a[p - i]) / (1 - k * k) for i in range(p)]\n    return {'stable': True, 'reflection': ks}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: negative leading coefficient', ['-2', '1', '-1/2'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['regression: random denominator 3', ['-1', '-1/2'], {'stable': True, 'reflection': ['1/2']}], ['regression: random denominator 4', ['-1', '0', '5/4'], {'stable': False, 'reflection': ['-5/4']}], ['control: marginal pole on unit circle', ['1', '0', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: stable second order', ['1', '-1/2', '1/4'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['control: trailing zero coefficient', ['1', '1/2', '0'], {'stable': True, 'reflection': ['1/2']}], ['control: two trailing zeros', ['1', '-1/3', '0', '0'], {'stable': True, 'reflection': ['-1/3']}]], [['regression: random denominator 6', ['1/2', '1/8'], {'stable': True, 'reflection': ['1/4']}], ['regression: random denominator 11', ['-1', '0', '-1/2'], {'stable': True, 'reflection': ['1/2', '0']}], ['regression: random denominator 4', ['-1', '0', '5/4'], {'stable': False, 'reflection': ['-5/4']}], ['control: pole at -1', ['1', '1'], {'stable': False, 'reflection': ['1']}], ['control: unstable first order', ['1', '-3/2'], {'stable': False, 'reflection': ['-3/2']}], ['control: bad a0', ['0', '1'], 'bad-a0'], ['control: third order', ['1', '-1/2', '1/3', '-1/5'], {'stable': True, 'reflection': ['-1/5', '35/144', '-65/179']}]], [['regression: random denominator 19', ['-1', '3/4'], {'stable': True, 'reflection': ['-3/4']}], ['regression: random denominator 21', ['1/2', '3/4'], {'stable': False, 'reflection': ['3/2']}], ['regression: random denominator 28', ['-1', '1/8'], {'stable': True, 'reflection': ['-1/8']}], ['control: random denominator 0', ['-1', '0'], {'stable': True, 'reflection': []}], ['control: random denominator 1', ['1', '1/8', '1/8'], {'stable': True, 'reflection': ['1/8', '1/9']}], ['control: random denominator 2', ['1', '1/3', '1/3'], {'stable': True, 'reflection': ['1/3', '1/4']}], ['control: random denominator 5', ['1', '1/8', '1/3'], {'stable': True, 'reflection': ['1/3', '3/32']}]], [['regression: random denominator 24', ['2', '1/2'], {'stable': True, 'reflection': ['1/4']}], ['regression: random denominator 27', ['2', '1/3', '-1/2', '1/8'], {'stable': True, 'reflection': ['1/16', '-40/153', '28/113']}], ['regression: random denominator 34', ['-1', '1/2', '-1', '0'], {'stable': False, 'reflection': ['1']}], ['control: random denominator 7', ['1', '3/4', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 8', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}], ['control: random denominator 9', ['1', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 10', ['1', '-1/4', '1/8', '-1/2'], {'stable': True, 'reflection': ['-1/2', '0', '-1/4']}]], [['regression: random denominator 32', ['1/2', '-1/2'], {'stable': False, 'reflection': ['-1']}], ['regression: random denominator 34', ['-1', '1/2', '-1', '0'], {'stable': False, 'reflection': ['1']}], ['regression: random denominator 52', ['-1', '3/4', '5/4', '-1'], {'stable': False, 'reflection': ['1']}], ['control: random denominator 12', ['1', '5/4', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 13', ['1', '1/8', '1/8', '3/4'], {'stable': True, 'reflection': ['3/4', '1/14', '1/15']}], ['control: random denominator 14', ['1', '1/8', '5/4'], {'stable': False, 'reflection': ['5/4']}], ['control: random denominator 15', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"50578328ff555ad91786d65fefb6e8c45defcdf140151693352b3f74e5596afc","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a = [Fraction(v) for v in x]\n    if not a or a[0] == 0:\n        return 'bad-a0'\n    a = [v / a[0] for v in a]\n    while len(a) > 1 and a[-1] == 0:\n        a.pop()\n    ks = []\n    while len(a) > 1:\n        p = len(a) - 1\n        k = a[p]\n        ks.append(str(k))\n        if abs(k) >= 1:\n            return {'stable': False, 'reflection': ks}\n        a = [(a[i] - k * a[p - i]) / (1 - k * k) for i in range(p)]\n    return {'stable': True, 'reflection': ks}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: negative leading coefficient', ['-2', '1', '-1/2'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['regression: random denominator 3', ['-1', '-1/2'], {'stable': True, 'reflection': ['1/2']}], ['regression: random denominator 4', ['-1', '0', '5/4'], {'stable': False, 'reflection': ['-5/4']}], ['control: marginal pole on unit circle', ['1', '0', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: stable second order', ['1', '-1/2', '1/4'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['control: trailing zero coefficient', ['1', '1/2', '0'], {'stable': True, 'reflection': ['1/2']}], ['control: two trailing zeros', ['1', '-1/3', '0', '0'], {'stable': True, 'reflection': ['-1/3']}]], [['regression: random denominator 6', ['1/2', '1/8'], {'stable': True, 'reflection': ['1/4']}], ['regression: random denominator 11', ['-1', '0', '-1/2'], {'stable': True, 'reflection': ['1/2', '0']}], ['regression: random denominator 4', ['-1', '0', '5/4'], {'stable': False, 'reflection': ['-5/4']}], ['control: pole at -1', ['1', '1'], {'stable': False, 'reflection': ['1']}], ['control: unstable first order', ['1', '-3/2'], {'stable': False, 'reflection': ['-3/2']}], ['control: bad a0', ['0', '1'], 'bad-a0'], ['control: third order', ['1', '-1/2', '1/3', '-1/5'], {'stable': True, 'reflection': ['-1/5', '35/144', '-65/179']}]], [['regression: random denominator 19', ['-1', '3/4'], {'stable': True, 'reflection': ['-3/4']}], ['regression: random denominator 21', ['1/2', '3/4'], {'stable': False, 'reflection': ['3/2']}], ['regression: random denominator 28', ['-1', '1/8'], {'stable': True, 'reflection': ['-1/8']}], ['control: random denominator 0', ['-1', '0'], {'stable': True, 'reflection': []}], ['control: random denominator 1', ['1', '1/8', '1/8'], {'stable': True, 'reflection': ['1/8', '1/9']}], ['control: random denominator 2', ['1', '1/3', '1/3'], {'stable': True, 'reflection': ['1/3', '1/4']}], ['control: random denominator 5', ['1', '1/8', '1/3'], {'stable': True, 'reflection': ['1/3', '3/32']}]], [['regression: random denominator 24', ['2', '1/2'], {'stable': True, 'reflection': ['1/4']}], ['regression: random denominator 27', ['2', '1/3', '-1/2', '1/8'], {'stable': True, 'reflection': ['1/16', '-40/153', '28/113']}], ['regression: random denominator 34', ['-1', '1/2', '-1', '0'], {'stable': False, 'reflection': ['1']}], ['control: random denominator 7', ['1', '3/4', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 8', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}], ['control: random denominator 9', ['1', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 10', ['1', '-1/4', '1/8', '-1/2'], {'stable': True, 'reflection': ['-1/2', '0', '-1/4']}]], [['regression: random denominator 32', ['1/2', '-1/2'], {'stable': False, 'reflection': ['-1']}], ['regression: random denominator 34', ['-1', '1/2', '-1', '0'], {'stable': False, 'reflection': ['1']}], ['regression: random denominator 52', ['-1', '3/4', '5/4', '-1'], {'stable': False, 'reflection': ['1']}], ['control: random denominator 12', ['1', '5/4', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 13', ['1', '1/8', '1/8', '3/4'], {'stable': True, 'reflection': ['3/4', '1/14', '1/15']}], ['control: random denominator 14', ['1', '1/8', '5/4'], {'stable': False, 'reflection': ['5/4']}], ['control: random denominator 15', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic bounded teaching model with a stipulated toy contract; exact rational arithmetic or fixed-decimal rounding keeps outputs strict JSON. It is not a production DSP library and claims no standards conformance. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-digital_signal_filters-schur-cohn-stability-leading-coefficient-normalization","generated_at":"2026-09-29T14:51:37.482218+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Checking IIR denominators for stability before deployment prevents runaway filters; step-down slips accept unstable designs.","repair":"Divide every coefficient by a0 first.","root_cause":"The polynomial is used without dividing by a0.","sha256":"ef17257db0394896bc131591e90c42dcffc26fd1dbc615199fe8c927b3236c73","title":"Stability test skips normalization by a0 · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.396,"exit_code":1,"observations":[{"actual":{"reflection":["-1/4","2/3"],"stable":true},"check":"regression: negative leading coefficient","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":false},{"actual":{"reflection":["-1/2"],"stable":true},"check":"regression: random denominator 3","expected":{"reflection":["1/2"],"stable":true},"passed":false},{"actual":{"reflection":["5/4"],"stable":false},"check":"regression: random denominator 4","expected":{"reflection":["-5/4"],"stable":false},"passed":false},{"actual":{"reflection":["-1"],"stable":false},"check":"control: marginal pole on unit circle","expected":{"reflection":["-1"],"stable":false},"passed":true},{"actual":{"reflection":["1/4","-2/5"],"stable":true},"check":"control: stable second order","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":true},{"actual":{"reflection":["1/2"],"stable":true},"check":"control: trailing zero coefficient","expected":{"reflection":["1/2"],"stable":true},"passed":true},{"actual":{"reflection":["-1/3"],"stable":true},"check":"control: two trailing zeros","expected":{"reflection":["-1/3"],"stable":true},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: negative leading coefficient\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/4\", \"2/3\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": false}, {\"check\": \"regression: random denominator 3\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"passed\": false}, {\"check\": \"regression: random denominator 4\", \"actual\": {\"stable\": false, \"reflection\": [\"5/4\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"-5/4\"]}, \"passed\": false}, {\"check\": \"control: marginal pole on unit circle\", \"actual\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"passed\": true}, {\"check\": \"control: stable second order\", \"actual\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": true}, {\"check\": \"control: trailing zero coefficient\", \"actual\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"passed\": true}, {\"check\": \"control: two trailing zeros\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.317,"exit_code":1,"observations":[{"actual":{"reflection":["-1/2","2"],"stable":false},"check":"regression: negative leading coefficient","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":false},{"actual":{"reflection":["-1/2"],"stable":true},"check":"regression: random denominator 3","expected":{"reflection":["1/2"],"stable":true},"passed":false},{"actual":{"reflection":["5/4"],"stable":false},"check":"regression: random denominator 4","expected":{"reflection":["-5/4"],"stable":false},"passed":false},{"actual":{"reflection":["-1"],"stable":false},"check":"control: marginal pole on unit circle","expected":{"reflection":["-1"],"stable":false},"passed":true},{"actual":{"reflection":["1/4","-2/5"],"stable":true},"check":"control: stable second order","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":true},{"actual":{"reflection":["1/2"],"stable":true},"check":"control: trailing zero coefficient","expected":{"reflection":["1/2"],"stable":true},"passed":true},{"actual":{"reflection":["-1/3"],"stable":true},"check":"control: two trailing zeros","expected":{"reflection":["-1/3"],"stable":true},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: negative leading coefficient\", \"actual\": {\"stable\": false, \"reflection\": [\"-1/2\", \"2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": false}, {\"check\": \"regression: random denominator 3\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"passed\": false}, {\"check\": \"regression: random denominator 4\", \"actual\": {\"stable\": false, \"reflection\": [\"5/4\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"-5/4\"]}, \"passed\": false}, {\"check\": \"control: marginal pole on unit circle\", \"actual\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"passed\": true}, {\"check\": \"control: stable second order\", \"actual\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": true}, {\"check\": \"control: trailing zero coefficient\", \"actual\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"passed\": true}, {\"check\": \"control: two trailing zeros\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.883,"exit_code":0,"observations":[{"actual":{"reflection":["1/4","-2/5"],"stable":true},"check":"regression: negative leading coefficient","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":true},{"actual":{"reflection":["1/2"],"stable":true},"check":"regression: random denominator 3","expected":{"reflection":["1/2"],"stable":true},"passed":true},{"actual":{"reflection":["-5/4"],"stable":false},"check":"regression: random denominator 4","expected":{"reflection":["-5/4"],"stable":false},"passed":true},{"actual":{"reflection":["-1"],"stable":false},"check":"control: marginal pole on unit circle","expected":{"reflection":["-1"],"stable":false},"passed":true},{"actual":{"reflection":["1/4","-2/5"],"stable":true},"check":"control: stable second order","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":true},{"actual":{"reflection":["1/2"],"stable":true},"check":"control: trailing zero coefficient","expected":{"reflection":["1/2"],"stable":true},"passed":true},{"actual":{"reflection":["-1/3"],"stable":true},"check":"control: two trailing zeros","expected":{"reflection":["-1/3"],"stable":true},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: negative leading coefficient\", \"actual\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": true}, {\"check\": \"regression: random denominator 3\", \"actual\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"passed\": true}, {\"check\": \"regression: random denominator 4\", \"actual\": {\"stable\": false, \"reflection\": [\"-5/4\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"-5/4\"]}, \"passed\": true}, {\"check\": \"control: marginal pole on unit circle\", \"actual\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"passed\": true}, {\"check\": \"control: stable second order\", \"actual\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": true}, {\"check\": \"control: trailing zero coefficient\", \"actual\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"passed\": true}, {\"check\": \"control: two trailing zeros\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}